
We set \(d = 4\) , \(n_1 = n_2 = n_3 = n_4 = 20\) . The above function-related tensors possess a property that the singular values of their unfolding formats delay sufficiently fast but do not become exactly zero. It implies that the underlying tensors are not precisely low rank. To improve the reconstruction quality for these data, we adopt
the rank-increasing strategy proposed in [1]} for the tested algorithms. For more details about the rank-increasing procedure, we refer the reader to [1]}. The maximum rank is set to \(\mathbf {r}= \left(1,5,5,5,1\right)\) . Tested algorithms are terminated at each rank-increasing step whenever the relative residual \(\frac{\left\Vert  {\cal P}_{\Omega }\left({\cal X}_t\right)-{\cal P}_{\Omega }\left({\cal T}\right)\right\Vert _{{\footnotesize {\mathsf {F}}}}}{\left\Vert  {\cal P}_{\Omega }\left({\cal T}\right)\right\Vert _{{\footnotesize {\mathsf {F}}}}}\)  is less than \( 10^{-5}\) , or 15 (20 at final step) number of iterations are reached, or the relative change \(\frac{\vert \left\Vert  {\cal P}_{\Omega }\left({\cal X}_t\right)-{\cal P}_{\Omega }\left({\cal T}\right)\right\Vert _{{\footnotesize {\mathsf {F}}}}-\left\Vert  {\cal P}_{\Omega }\left({\cal X}_{t-1}\right)-{\cal P}_{\Omega }\left({\cal T}\right)\right\Vert _{{\footnotesize {\mathsf {F}}}}\vert }{\left\Vert  {\cal P}_{\Omega }\left({\cal X}_{t-1}\right)-{\cal P}_{\Omega }\left({\cal T}\right)\right\Vert _{{\footnotesize {\mathsf {F}}}}}\)  is less than \( 10^{-3}\) .
